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Experimental data is often affected by uncontrolled variables that makeanalysis and interpretation difficult. For spatiotemporal systems, this problemis further exacerbated by their intricate dynamics. Modern machine learningmethods are particularly well-suited for analyzing and modeling complexdatasets, but to be effective in science, the result needs to be interpretable.We demonstrate an unsupervised learning technique for extracting interpretablephysical parameters from noisy spatiotemporal data and for building atransferable model of the system. In particular, we implement aphysics-informed architecture based on variational autoencoders that isdesigned for analyzing systems governed by partial differential equations(PDEs). The architecture is trained end-to-end and extracts latent parametersthat parameterize the dynamics of a learned predictive model for the system. Totest our method, we train our model on simulated data from a variety of PDEswith varying dynamical parameters that act as uncontrolled variables. Numericalexperiments show that our method can accurately identify relevant parametersand extract them from raw and even noisy spatiotemporal data (tested withroughly 10% added noise). These extracted parameters correlate well (linearlywith $R^2 > 0.95$) with the ground truth physical parameters used to generatethe datasets. We then apply this method to nonlinear fiber propagation data,generated by an ab-initio simulation, to demonstrate its capabilities on a morerealistic dataset. Our method for discovering interpretable latent parametersin spatiotemporal systems will allow us to better analyze and understandreal-world phenomena and datasets, which often have unknown and uncontrolledvariables that alter the system dynamics and cause varying behaviors that aredifficult to disentangle.

Extracting Interpretable Physical Parameters from Spatiotemporal Systems using Unsupervised Learning